Local Trajectory Variation Exponent (LTVE) for Visualizing Dynamical Systems (Communications in Computational Physics, 2024)
The identification and visualization of Lagrangian structures in flows playsa crucial role in the study of dynamic systems and fluid dynamics. The Finite TimeLyapunov Exponent (FTLE) has been widely used for this purpose; however, it onlyapproximates the flow by considering the positions of particles at the initial and finaltimes, ignoring the actual trajectory of the particle. To overcome this limitation, wepropose a novel quantity that extends and generalizes the FTLE by incorporating trajectory metrics as a measure of similarity between trajectories. Our proposed methodutilizes trajectory metrics to quantify the distance between trajectories, providing amore robust and accurate measure of the LCS. By incorporating trajectory metrics, wecan capture the actual path of the particle and account for its behavior over time, resulting in a more comprehensive analysis of the flow. Our approach extends the traditionalFTLE approach to include trajectory metrics as a means of capturing the complexity ofthe flow.
Keywords: Lagrangian coherent structure; trajectory metric; trajectory analysis; finite time Lyapunov exponent.